Ten years ago this week thousands of people were queueing outside Northern Rock to take all their money out. A decade on, 25,000 people are currently queueing to put their money into a bank – one that appears to have won an almost cultish following among young adults.

Anyone without a smartphone (and even most of those with one) and anyone over 40 years old is likely to be unaware of the Monzo phenomenon. So excited are young adults about this new bank account (that’s right, young people excited about a bank account) that they are clambering to join. About 400,000 have already done so, happily coughing up a £100 deposit rather than taking the £100 giveaway that other banks hand out to new customers, while a further 25,000 are waiting to get in the door. Meanwhile, the 32-year-old who runs it, Tom Blomfield, confidently predicts one billion customers in five years’ time as Monzo, or something like it, becomes the “control hub” for all your financial arrangements, from savings to spending, from current accounts to utilities. And yes, he did say one billion rather than one million.

Jaded personal finance hacks, on first seeing the Monzo launch – it only obtained its full banking licence in April – gave it a bit of a “so what” response. Another “challenger” bank. Another online provider. Another app-based player. Yawn. But Monzo appears to have caught the zeitgeist.

On the face of it Monzo has only limited appeal, particularly against the likes of Nationwide or First Direct. There are no set-up or usage fees, and there are zero charges for spending abroad. But there are no branches and no mortgages or savings accounts – just a prepaid MasterCard. But Blomfield claims that for people who spend their lives on their smartphones, it’s more than a conventional bank. “It’s much more emotional. A lot of young people feel anxious and stressful about money. They lose track of their spending, with some payments taking three or four days to appear, so they exceed their overdraft. What Monzo does is auto-budget for you. It tells you how much you’re spending, say, on eating out. It’s really easy to send and receive money – so if four of you are in a restaurant it splits the bill instantly.

“We’ll be moving on to gas and electricity companies – we’ll have smart software that optimises your spending. You kinda know you should be switching here and there to find the best deal, but life gets in the way. With Monzo we auto-switch you to the best deal. For example, we don’t offer our own savings account – we’ll just put [your money] in the best Isa or savings account for you.” Monzo says it will use new open banking rules to act as the hub for all your accounts.

The enthusiasm for it is remarkable. One 26-year-old I spoke to this week was gushing about how “all my friends have it. They love it. It tells you straightaway exactly how much money you have to spend, and what you’re overspending on.” She fits the Monzo profile perfectly: a university graduate who works in London at an internet-based firm where almost no one is over 40. But she doesn’t even have it yet. She’s in the queue.

Christopher Theodorou, 34, who lives in north London, signed up for Monzo in January and is another big fan. “I’ve been using it for a solid seven to eight months and really like it. As of May I’ve started essentially making all my everyday payments using it.” He loves the way the app lets you keep tabs on what you’re spending your money on, and the fact that when any money is taken off the card you immediately get a push notification to your mobile phone.

But in July Monzo reported losses of nearly £7m. Blomfield casually admits he’ll burn through far more than that before making a profit. This could crash and burn like so many other start-ups. Or be gobbled up by Google. Or we may be genuinely seeing the new face of banking.